Electrical Circuits & Course Information

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Questions and Answers

Which of the following activities is explicitly discouraged during lectures, based on the provided guidelines?

  • Taking notes on a laptop
  • Using a mobile phone for any purpose (correct)
  • Engaging in group discussions related to the topic
  • Asking clarifying questions to the lecturer

An electric circuit is best described as:

  • An interconnected set of elements providing a closed path for current flow. (correct)
  • An open path allowing for the free flow of electrons.
  • A collection of electrical components that may or may not be connected.
  • Any arrangement of wires and electronic components.

Which of the following components is classified as an active element in an electrical circuit?

  • Solar Cell (correct)
  • Inductor
  • Resistor
  • Capacitor

What is the weighting of the mid-semester examination towards the final grade in the Telecommunications Engineering course?

<p>30% (C)</p> Signup and view all the answers

According to the course outline, which topic is covered immediately after Network Theorems?

<p>AC Circuits (B)</p> Signup and view all the answers

Which type of activity is part of the course delivery method?

<p>Circuit Design (B)</p> Signup and view all the answers

If a student scores 65% on the end-of-semester examination, what is the contribution of this score to the final course grade?

<p>45.5% (A)</p> Signup and view all the answers

Which of the following is NOT explicitly listed as an element of an electric circuit?

<p>Transistors (C)</p> Signup and view all the answers

Based on the figures provided, which statement accurately describes the arrangement of resistors R1 and R2 in Figure 1?

<p>R1 and R2 are in series, with the same current flowing through them. (B)</p> Signup and view all the answers

In the context of the content, what is a key characteristic that defines resistors as being in parallel?

<p>The voltage drop across each resistor is the same. (B)</p> Signup and view all the answers

According to the material, which of the following correctly calculates the total resistance ($R_T$) of N resistors connected in series?

<p>$R_T = R_1 + R_2 + ... + R_N$ (D)</p> Signup and view all the answers

Given three resistors with resistances of 1Ω each, connected in parallel, and then in series with another 1Ω resistor, followed by another two 1Ω resistors connected in parallel. What is the total equivalent resistance?

<p>27/8 Ω (C)</p> Signup and view all the answers

Using the 'circling' method described, which criterion must be met for two resistors to be considered in parallel?

<p>It should be possible to move from one resistor to the other without passing through another circuit element. (C)</p> Signup and view all the answers

In a parallel circuit with two resistors, $R_1$ and $R_2$, if the total current entering the parallel branch is I, which expression correctly describes the current $I_1$ flowing through resistor $R_1$?

<p>$I_1 = I * (R_2 / (R_1 + R_2))$ (C)</p> Signup and view all the answers

Consider a circuit with three resistors: $R_1 = 10\Omega$, $R_2 = 20\Omega$, and $R_3 = 30\Omega$, all connected in series. What is the total resistance of the circuit?

<p>60$\Omega$ (A)</p> Signup and view all the answers

Two resistors, $R_1 = 10Ω$ and $R_2 = 20Ω$, are connected in parallel. If the total current entering the parallel combination is 3A, what is the current flowing through $R_2$?

<p>1 A (A)</p> Signup and view all the answers

In a parallel circuit with two resistors, $R_1$ and $R_2$, if $R_1$ is much larger than $R_2$, what can be generally said about the equivalent resistance ($R_{eq}$) of the parallel combination?

<p>$R_{eq}$ will be approximately equal to $R_2$. (B)</p> Signup and view all the answers

Which of the following statements regarding the application of the current division rule is most accurate?

<p>It applies only to parallel circuits and is used to find the current through each resistor. (D)</p> Signup and view all the answers

A circuit contains a series combination of a 5$\Omega$ resistor and an unknown resistor, R. If the voltage source is 12V and the current flowing through the circuit is 2A, what is the value of the unknown resistor R?

<p>1$\Omega$ (D)</p> Signup and view all the answers

Consider a scenario where three resistors, each with a resistance of 12$\Omega$, are connected in parallel. Calculate the equivalent resistance of this parallel combination.

<p>4$\Omega$ (B)</p> Signup and view all the answers

In a circuit with two parallel resistors, if the current flowing through one resistor increases, while the total current entering the parallel combination remains constant, what happens to the current flowing through the other resistor?

<p>It decreases to maintain the constant total current. (D)</p> Signup and view all the answers

Consider a parallel circuit with two resistors, $R_1$ and $R_2$. If $R_1$ is significantly larger than $R_2$, how will the current divide between them?

<p>Most of the current will flow through $R_2$. (C)</p> Signup and view all the answers

What key principle underlies the current division rule in parallel circuits?

<p>The current distributes itself inversely proportional to the resistance of each branch. (C)</p> Signup and view all the answers

Two resistors $R_1$ and $R_2$ are in parallel. If $R_1 = R_2 = R$, and a current I enters the parallel combination, what is the current through $R_1$?

<p>I/2 (C)</p> Signup and view all the answers

Using Kirchhoff's Current Law (KCL), determine the value of current 'i' in the circuit if the incoming currents are 5A and 3A, and the outgoing currents, excluding 'i', are 4A and 2A.

<p>i = 0A (A)</p> Signup and view all the answers

In a closed-loop circuit, a voltage source $V_1$ is connected in series with resistors $R_1$ and $R_2$. If the voltage drop across $R_1$ is 5V and the voltage drop across $R_2$ is 3V, what is the value of $V_1$ according to Kirchhoff's Voltage Law (KVL)?

<p>$V_1 = 8V$ (A)</p> Signup and view all the answers

Consider a circuit loop with a 12V voltage source and three resistors in series. If two of the resistors have voltage drops of 4V and 5V respectively, what is the voltage drop across the third resistor, according to Kirchhoff's Voltage Law (KVL)?

<p>3V (B)</p> Signup and view all the answers

In a circuit, a node has three branches. Two branches have currents entering the node with values of 2A and 3A. If the third branch has a current leaving the node, what is its value according to Kirchhoff's Current Law (KCL)?

<p>5A (D)</p> Signup and view all the answers

A closed circuit loop contains a 9V battery and two resistors. If the current flowing through the loop is 1A and one resistor has a resistance of 4 ohms, what is the resistance of the other resistor?

<p>R = 5 ohms (D)</p> Signup and view all the answers

In a series circuit with a voltage source $V$, two resistors $R_1$ and $R_2$ are connected. If the current through the circuit is 'I', which equation correctly represents Kirchhoff's Voltage Law (KVL) for this circuit?

<p>$V - IR_1 - IR_2 = 0$ (A)</p> Signup and view all the answers

A parallel circuit has two branches connected to a common node. If the current entering the node is 7A, and one branch has a current of 3A, what is the current in the other branch according to Kirchhoff's Current Law (KCL)?

<p>4A (B)</p> Signup and view all the answers

Consider a circuit loop with two voltage sources, $V_1 = 6V$ and $V_2 = 3V$, oriented such that they oppose each other. If there is a single resistor $R$ in the loop with a current $I = 1A$ flowing through it, what is the resistance $R$ according to Kirchhoff's Voltage Law (KVL)?

<p>R = 3 ohms (D)</p> Signup and view all the answers

Using the provided circuit and calculations, what is the value of $I_1$?

<p>0.2 A (B)</p> Signup and view all the answers

Based on the circuit analysis, what is the value of $I_2$?

<p>0.3 A (D)</p> Signup and view all the answers

What is the calculated Thevenin voltage ($V_{TH}$) for the circuit?

<p>2.7 V (B)</p> Signup and view all the answers

What is the equivalent resistance of two parallel resistors with values of 5 Ω and 15 Ω?

<p>3.75 Ω (B)</p> Signup and view all the answers

What is the calculated Thevenin resistance ($R_{TH}$) for the circuit?

<p>9.25 Ω (D)</p> Signup and view all the answers

If the 5Ω resistor was changed to a short circuit, how would this affect the calculation of $I_1$?

<p>$I_1$ would increase (C)</p> Signup and view all the answers

If the 12Ω resistor was changed to an open circuit, how would this affect the calculation of $I_2$?

<p>$I_2$ would become zero (B)</p> Signup and view all the answers

Using the Superposition Theorem, what is the correct process for finding the current through a resistor in a circuit with multiple voltage sources?

<p>Determine the current due to each voltage source acting alone, and then sum these individual currents algebraically. (A)</p> Signup and view all the answers

In the Superposition Theorem example given, what is the significance of calculating $I_A$ and $I_B$?

<p>They are intermediate currents used to compute the total current through a specific branch when each voltage source is considered independently. (B)</p> Signup and view all the answers

Given the Superposition Theorem example, if the 42V source was doubled and the 35V source was removed, what would be the new current I in the $3\Omega$ resistor, assuming $I_A$ doubles as well?

<p>-3A (A)</p> Signup and view all the answers

The Reciprocity Theorem is applicable to which type of network?

<p>Only linear, time-invariant networks. (D)</p> Signup and view all the answers

In the context of the Reciprocity Theorem, what is meant by 'interchanging' an ideal ammeter and an ideal voltage source?

<p>Moving the voltage source to the branch where the ammeter was, and placing the ammeter in series with the original voltage source. (A)</p> Signup and view all the answers

According to the Reciprocity Theorem, what condition must be met for the theorem to hold true when interchanging an ideal ammeter and an ideal voltage source?

<p>The reading of the ammeter must remain unchanged after the interchange. (A)</p> Signup and view all the answers

Consider a circuit with a voltage source V(t), resistors R1, R2, and R3, and an ammeter A. If the voltage source is 10V and the ammeter reads 2A before the interchange, what should the ammeter read after the voltage source and ammeter are interchanged, assuming the Reciprocity Theorem holds?

<p>2A (B)</p> Signup and view all the answers

What is a key assumption about the ammeter and voltage source for the Reciprocity Theorem to hold true?

<p>They must be ideal, with zero internal resistance for the ammeter and zero internal impedance for the voltage source. (A)</p> Signup and view all the answers

Flashcards

What is a circuit?

An interconnection of elements forming a closed path allowing current flow.

Active elements

Energy-producing components in a circuit.

Passive elements

Energy-consuming components in a circuit.

Examples of passive elements

Resistors, inductors, and capacitors.

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Examples of active elements

Batteries, generators, and solar cells.

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What are Network Theorems?

A systematic way to simplify and analyze complex circuits.

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What are AC Circuits?

Electrical circuits with sources that produce alternating current.

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What are 3-Phase Circuits?

Power distribution system using three alternating currents.

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Resistors in Series

Components connected end-to-end along a single path.

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Non-Series Resistors

Resistors are NOT configured in series if there are any branching points between them.

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Total Resistance (Series)

The total resistance in a series circuit is the sum of all individual resistances.

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Resistors in Parallel

Components connected across the same two points, having the same voltage.

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Identifying Parallel Resistors

Two resistors are in parallel if you can trace a path from one to the other without passing through another component.

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Voltage in Parallel Resistors

Resistors are in parallel when the voltage across them is the same.

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Current in Series Resistors

Two resistors are in series if all of the current that flows through one resistor also flows through the other resistor.

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Equivalent Resistance of Series Resistors

The equivalent resistance is the sum of each individual resistance.

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Current Division Rule

A rule for determining how current is divided between parallel branches in a circuit.

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RT in Current Division

The total resistance of parallel resistors before applying current division.

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I1 in Current Division

The current flowing through resistor R1 when current divides between R1 and R2.

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I2 in Current Division

The current flowing through resistor R2 when current divides between R1 and R2.

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Formula for I1

I1 equals total current multiplied by R2 divided by the sum of R1 and R2.

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Formula for I2

I2 equals total current multiplied by R1 divided by the sum of R1 and R2.

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Voltage, V

The voltage across parallel branches in a circuit, before applying current division.

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Negative Current

Current flows in the opposite direction and is noted with a negative symbol.

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Kirchhoff's Current Law (KCL)

Current entering a junction equals the current leaving it.

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Kirchhoff's Voltage Law (KVL)

The algebraic sum of voltages in a closed loop is zero.

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Loop (Closed Path)

A closed conducting path in an electrical circuit.

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Loop Analysis

Analyzing circuits by applying KVL around defined loops.

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KVL Alternative Definition

The sum of voltage sources equals the sum of voltage drops.

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Resistor

A component that reduces or opposes the flow of electrical currrent.

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Voltage Drop

Voltage drop across resistor R due to current I.

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Circuit Analysis

Using KCL and KVL to determine unknown currents and voltages.

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What is Thevenin Voltage (VTH)?

The voltage across terminals A and B in a simplified circuit.

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What is Thevenin Resistance (RTH)?

The resistance looking back from terminals A and B with all independent sources turned off.

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What is Thevenin's Theorem?

A method to simplify a complex circuit into a voltage source (VTH) and a series resistance (RTH).

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What is KVL?

Kirchhoff's Voltage Law. The sum of voltages around any closed loop is zero.

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What is I1?

The current flowing through the 15Ω resistor when solving for VTH.

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What is I2?

The current flowing through the 8Ω resistor when solving for VTH.

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What are Series Resistors?

Resistors connected end-to-end, so the same current flows through each.

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What are Parallel Resistors?

Resistors connected across each other, so the voltage across them is the same

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Superposition Theorem

A theorem used to find the current in a circuit with multiple sources by considering the effect of each source independently.

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Applying Superposition

In the Superposition Theorem, each independent source is considered alone while other voltage sources are short-circuited and current sources are open-circuited.

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Acting Alone: 35V Battery

With only the 35V battery acting, the total resistance is calculated to find the total current.

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Reciprocity Theorem

A theorem stating that the position of an ideal ammeter and an ideal voltage source can be interchanged in a linear network without changing the ammeter reading.

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Ammeter and Voltage Source

An ideal ammeter and an ideal voltage source can be interchanged

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Linear Network

A network with components and sources where the principle of superposition holds is called a Linear Network

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Deactivating Sources

When using the Superposition Theorem, voltage sources are short-circuited, and current sources are open-circuited when they are not being considered.

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Batteries Acting

When both batteries are acting, the resulting current ,I, is calculated by subtracting IA from IB.

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Study Notes

  • Electrical Engineering 151: Applied Electricity is being instructed by Ing. Dr. Abdul-Rahman Ahmed in 2018
  • Contact the course instructor at [email protected] or call 0508 - 351 - 438
  • The course material link is https://www.rfmicrowaveknust.com
  • The Teaching Assistants are Akambole Isaac Ageebase and Alberta Oduraa Quartey
  • Akambole Isaac Ageebase can be reached at [email protected] or 0506257842
  • Alberta Oduraa Quartey can be reached by calling 0547886101 or emailing [email protected]
  • Appreciate basic principles of Electrical Circuits
  • Tools are required to be able to analyze electric and magnetic circuits
  • The goal is to develop knowledge and fundamental concepts associated with Electrical/Electronics Engineering

Course Outline Includes

  • Circuits and Network Theorems
  • Alternating current circuits
  • Three-phase circuits
  • Magnetic circuits

Course Calendar

  • 3rd September - Network Theorems
  • 10th September - Network Theorems
  • 17th September - AC Circuits
  • 24th September - AC Circuits
  • 1st October - 3-Phase Circuits
  • 8th October - 3-Phase Circuits
  • 15th October - Magnetic Circuits
  • 22nd October - Revision/Tutorial
  • 29th October - Revision/Tutorial
  • 5th November - Mid-Semester Exams
  • 19th November - Magnetic Circuits
  • 26th November - Revision/Tutorial
  • 3rd December - End of Semester Exams (to be confirmed)
  • Lectures will be given, along with Tutorials, Circuit Design, Simulations and Laboratory work

Classroom rules include

  • No phone usage
  • No eating
  • No noise-making
  • No lateness
  • No gossiping
  • No sleeping
  • Course grade is based on Quizzes (30%) and Mid-semester examination (30%) for 60%
  • End of semester examination makes up 70% of the final grade

Unit 1: Circuit and Network Theorems

  • An interconnection of elements forming a closed path along which current can flow is a circuit
  • Active elements produce energy ex. Batteries, Generators, solar cells etc.
  • Passive elements use element's energy ex. Resistors, inductors, capacitors
  • A point where currents split or come together is a node
  • A connection where current flows is the path
  • A connection between two nodes is a branch
  • A closed path of a circuit loop/mesh
  • A branch of theoretically zero resistance is a Short-circuit
  • Short-circuits divert to itself all currents that would have flown in adjacent branches and are hooked to the same node as the short except for other branches with sources
  • A branch of theoretically infinite resistance, preventing current flow is an open circuit
  • Resistors are in series if the same current flows through them
  • Total R for resistors R1, R2, R3, ...., R, which are in series: RT =R₁+R₂+R+....+R
  • Resistors in parallel have the same voltage across them
  • If two resistors are able to move from one to the other without passing through another element, i.e., the two can be circled, they are in parellel

Equation for for 2 resistors in parallel:

  • 1/RT = 1/R₁ + 1/R₂ so RT = (R₁R₂)/(R₁ + R₂)
  • Effective circuit resistance is found by identifying series and parallel resistors and putting them together

Current Division Rule

  • Applied to share current between parallel branches
  • In summary of Current Division Rule:    For R1 in parallel with R2:        I1 = I(R2 /(R1 + R2))       I2 = I(R1 /(R1 + R2))
  • Voltage Drop from I = to V-V1

Kirchhoff's Current Law (KCL)

  • Sum of currents entering a node equals the sum of currents leaving the node

Kirchhoff's Voltage Law (KVL)

  • The algebraic sum of the voltages in a loop (closed path) equals zero
  • Alternatively, in a loop, the algebraic sum of voltage sources equals the algebraic sum of voltage drops

Thevenin's Theorem

  • Any linear circuit connected between two terminals can be replaced by a Thevenin's voltage (VTH) in series with a Thevenin's resistance (RTH)
  • VTH is the open-circuit voltage across the two terminals
  • RTH is the resistance seen from the two terminals when all sources have been deactivated
  • Deactivate voltage sources by short circuiting them
  • Deactivate open circuit current sources

Steps in Thevenin's Equation

  1. Remove the resistor from the circuit and mark the two terminals.
  2. Find the open-circuit voltage (VTH) across the two terminals by applying KVL. Treat VTH as a source
  3. Recall the circuit created before step 2 and deactivate all sources. Short-circuit voltage sources
  4. Find the total resistance of the circuit resulting from step 3 as seen from1wo terminals
  5. Reproduce the Thevenin's equivalent circuit and connect the resistor whose current is to be found.
  6. Calculate the current in the circuit in step 5.
  • The Norton Theorem
    • Any linear circuit connected between two terminals can be replaced by a Norton's current (I)  in parallel with a Norton's resistance (RN)
    • RN is the resistance seen from the two terminals when all sources have been deactivated
    • The current Norton theorem IN=(V-V1)/R

Steps in Norton's Theorem

  1. Remove the resistor from the circuit and mark the two terminals
  2. Find the short-circuit current (I) through the two terminals by applying KVL
  3. Recall the circuit created before step 2 and Deactivate all short-circuit voltage sources and open-circuit current sources
  4. Find the total resistance of the circuit resulting from step 3
  5. Reproduce the Norton's equivalent circuit and connect the resistor whose current is to be found
  6. Calculate the current in the circuit in step 5

Superposition Theorem

  • The current or voltage across any element in a multiple-source linear circuit can be found by taking the algebraic sum of the current or voltage element due to each individual source while acting alone.

Reciprocity Theorem: 

  • An ideal ammeter and ideal voltage source can be interchanged in two different branches of a linear network, without changing the reading of the ammeter

Delta-star Transformation

A transformation is employed in situations where series nor parallel arrangements can be identified. Delta arrangement: - An arrangement of three (3) resistors where one terminal of a resistor is connected to another resistor and the terminal to a different resistor Star(Wye) arrangement: -An arrangement of three (3) resistors where all resistors have a common point of connection through one terminal of each resistor while the remaining terminals are unconnected

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